%0 Journal Article
%T W^*-derived sets of transfinite order of subspaces of dual Banach spaces
%A Mikhail I. Ostrovskii
%J Mathematics
%D 1993
%I arXiv
%X It is an English translation of the paper originally published in Russian and Ukrainian in 1987. In the appendix of his book S.Banach introduced the following definition Let $X$ be a Banach space and $\Gamma$ be a subspace of the dual space $X^*$. The set of all limits of $w^{*}$-convergent sequences in $\Gamma $ is called the $w^*${\it -derived set} of $\Gamma $ and is denoted by $\Gamma _{(1)}$. For an ordinal $\alpha$ the $w^{*}$-{\it derived set of order} $\alpha $ is defined inductively by the equality: $$ \Gamma _{(\alpha )}=\bigcup _{\beta <\alpha }((\Gamma _{(\beta )})_{(1)}. $$
%U http://arxiv.org/abs/math/9303203v1